We are interested in a graph-based Knowledge Representation formalism that would allow for the representation, manipulation, query, and reasoning over dependency structures, and linguistic knowledge of the Explanatory and Combinatorial Dictionary in the Meaning-Text Theory framework. Neither the semantic web formalisms nor the conceptual graphs appear to be suitable for this task, and this led to the introduction of the new Unit Graphs framework. This paper first introduces the foundational concepts of this framework: Unit Graphs are defined over a support that contains: i) a hierarchy of unit types which is strongly driven by their actantial structure, ii) a hierarchy of circumstantial symbols, and iii) a set of unit identifiers. Then, this paper provides all of these objects with a model semantics that enables to define the notion of semantic consequence between Unit Graphs.